Raising and lowering operators for Askey-Wilson polynomials

Siddhartha Sahi

doi:10.3842/SIGMA.2007.002

Raising and lowering operators for Askey-Wilson polynomials

Siddhartha Sahi

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In this paper we describe two pairs of raising/lowering operators for Askey- Wilson polynomials, which result from constructions involving very different techniques. The first technique is quite elementary, and depends only on the "classical" properties of these polynomials, viz. the q-difference equation and the three term recurrence. The second technique is less elementary, and involves the one-variable version of the double affine Hecke algebra.

Original language	English (US)
Article number	002
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	3
DOIs	https://doi.org/10.3842/SIGMA.2007.002
State	Published - Jan 1 2007

All Science Journal Classification (ASJC) codes

Analysis
Mathematical Physics
Geometry and Topology

Keywords

Askey-Wilson polynomials
Double affine Hecke algebra
Lowering operators
Orthogonal polynomials
Raising operators
Root systems
Three term recurrence
q-difference equation

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10.3842/SIGMA.2007.002

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AB - In this paper we describe two pairs of raising/lowering operators for Askey- Wilson polynomials, which result from constructions involving very different techniques. The first technique is quite elementary, and depends only on the "classical" properties of these polynomials, viz. the q-difference equation and the three term recurrence. The second technique is less elementary, and involves the one-variable version of the double affine Hecke algebra.

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